On a semilinear parabolic equation arising in optical bistability

DOI10.1016/0022-247X(89)90116-9zbMath0678.35055MaRDI QIDQ1124050

Kenneth J. Brown, Achilles Tertikas

Publication date: 1989

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

plane wavemultiple solutionsGaussian distributionradially symmetricstable solutionstravelling wave solutionshooting argumentsoptical bistable systemsub- and super-solutionnon-radial positive solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability in context of PDEs (35B35) Geometric theory, characteristics, transformations in context of PDEs (35A30) Physical optics (78A10)

Cites Work

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• Spherically symmetric solutions of a reaction-diffusion equation
• Symmetry and related properties via the maximum principle
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• On the Existence of Positive Solutions for a Class of Semilinear Elliptic Boundary Value Problems
• On the Existence of Positive Solutions of Semilinear Elliptic Equations

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